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ISPH simulation of impact flow of circular cylinder over free surface porous media

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Abstract

This work adopts the ISPH method for handling the impact flow of a circular cylinder over a free surface flow saturated by the porous media. The novelty of this work is simulating the impact flow over different porous structures. Introducing the ISPH method can track the large deformation of the free surface throughout the water entrance of a circular cylinder. In the ISPH scheme, a semi-implicit velocity technique is employed with an implicit solution of pressure through the pressure Poisson equation. The Smagorinsky model is used for the turbulence stress and the non-Darcy model is implemented for a porous medium. The ISPH scheme is well validated in terms of the free-falling of a circular cylinder and evaluated pressure, and it has a favorable comparison with the experimental results. The performed simulations showed the significance of using porous media for free surface flow in controlling the free-falling of a circular cylinder and free surface deformation during the impact processes. The porosity parameter is the main factor in powering the porous resistance for the impact flow. The empirical parameter of the nonlinear forces of the porous media is effective in the porous structures.

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Abbreviations

\(a, b\) :

Linear and nonlinear factors

\(C_{r}\) :

Inertia parameter

\(g\) :

Gravitational acceleration \(({\text{m/s}}^{2} )\)

\(h\) :

Smoothing length

\(k\) :

Kinetic energy

\(m\) :

Particle mass

\(p\) :

Pressure \(\left( {{\text{Nm}}^{ - 2} } \right)\)

\(S_{IJ}\) :

Strain rate

\(t\) :

Time \(({\text{s}})\)

\({\mathbf{U}}\) :

The velocity vector of free fluid \(\left( {\text{m/s}} \right)\)

\(W\) :

Kernal function

\(\delta_{IJ}\) :

Kronecker delta

\(\varepsilon\) :

Porosity

\(\mu\) :

Viscosity

\(\gamma\) :

Relaxation coefficient

\(\nu\) :

Kinematic viscosity \(\left( {{\text{m}}^{2} {\text{s}}^{ - 1} } \right)\)

\(v_{T}\) :

Eddy viscosity

\(\rho\) :

Density \(\left( {{\text{kg/m}}^{3} } \right)\)

\({{\varvec{\uptau}}}\) :

Turbulence stress

\(f\) :

Free fluid

\(p\) :

Porous medium

\(D\) :

Darcian

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the Research Group Project under Grant Number (RGP. 2/42/44).

Funding

This article received funding from the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, through the Research Group Project under Grant Number (RGP. 2/42/44).

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Authors and Affiliations

  1. Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia

    Fawzia Awad, Zehba Raizah & Abdelraheem M. Aly

  2. Department of Mathematics, College of Science, Bisha University, Bisha, 67714, Saudi Arabia

    Fawzia Awad

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  1. Fawzia Awad
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Correspondence to Abdelraheem M. Aly.

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Awad, F., Raizah, Z. & Aly, A.M. ISPH simulation of impact flow of circular cylinder over free surface porous media. J Braz. Soc. Mech. Sci. Eng. 45, 324 (2023). https://doi.org/10.1007/s40430-023-04242-6

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